Browsing by Subject "G10"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Existence, Uniqueness, and Determinacy of Equilibria in Complete Security Markets with Infinite Dimensional Martingale Generator(Center for Economic Research, Department of Economics, University of Minnesota, 2002-12) Kusuda, KojiThere is a strong evidence that most of financial variables are better described by a combination of diffusion and jump processes. Considering such evidence, researchers have studied security market models with jumps, in particular, in the context of option pricing. In most of their models, jump magnitude is specified as a continuously distributed random variable at each jump time. Then, the dimensionality of martingale generator, which can be interpreted as the "number of sources of uncertainty" in markets is infinite, and no finite set of securities can complete markets. In security market economy with infinite dimensional martingale generator, no equilibrium analysis has been conducted thus far. We assume approximately complete markets (Bjork et al. [10] [11]) in which a continuum of bonds are traded and any contingent claim can be approximately replicated with an arbitrary precision. We introduce the notion of approximate security market equilibrium in which an agent is allowed to choose a consumption plan approximately supported with any prescribed precision. We prove that an approximate security market equilibrium in approximately complete markets can be identified with an Arrow-Debreu equilibrium. Then, we present sufficient conditions for the existence of equilibria in the case of stochastic differential utilities with Inada condition, and for the existence, uniqueness, and determinacy of equilibria in the case of additively separable utilities.Item Infinite-Horizon Optimal Hedging Under Cone Constraints(Center for Economic Research, Department of Economics, University of Minnesota, 1999-01) Huang, Kevin XiaodongWe address the issue of hedging in infinite horizon markets with a type of constraints that the set of feasible portfolio holdings forms a convex cone. We show that the minimum cost of hedging a liability stream is equal to its largest present value with respect to admissible stochastic discount factors, thus can be determined without finding an optimal hedging strategy. We solve for an optimal hedging strategy by solving a sequence of independent one-period hedging problems. We apply the results to a variety of trading restrictions and also show how the admissible stochastic discount factors can be characterized.